Question

Listed below are the speed ((mi/h) measured from the Southbound traffic on I-280. The

speed limit is 65 mph.

62, 61, 61, 57, 61, 54, 59, 58, 59, 69, 60, 67, 70, 72, and 75

1. Construct a 99% confidence interval.

2. What will happen to the width of the confidence interval if the confidence level is

increased to 99%? Explain

3.) What will happen to the accuracy of the estimate if the sample size is increased.

Answer 1

1)

first calculate mean and standard deviation of the sample data given

2)

As confidence level increases value of z also increases so increase in z value increases width of confidence interval

we can see from given C1 AND C2 as confidence level increases width also increases

hence confidence interval length directly proportional to confidence level

3)

if sample size increases we have more information,then our estimate is more accurate. As our sample size increases, the confidence in our estimate also increases,and our uncertainty decreases and we have greater accuracy